关于广义Muirhead平均的Schur幂凸性

对广义Muirhead平均的Schur-幂凸性进行了讨论,给出了判定Muirhead平均的Schur-幂凸性的充要条件.结果改进了Chu和Xia在相关文献中的主要结果,Chu和Xia的结果是结果的特例.     

Convexifactors, Generalized Convexity, and Optimality Conditions

The recently introduced notion of a convexifactor is further studied, and quasiconvex and pseudoconvex functions are characterized in terms of convexifactors. As an application to a chain rule, a necessary optimality condition is deduced for an inequality constrained mathematical programming problem.     

保凸C^1分段二次多项式插值方法

本导出了二次多项式保凸的充要条件,通过插值部分新节点,得到了一种新的保凸Ｃ＾１分段二镒多项式插值函数。     

一类对称函数的Schur-几何凸性Schur-调和凸性

讨论一类对称函数的Schur-几何凸性和Schur-调和凸性.作为应用,利用控制理论,也得到一些新的分析不等式.     

Existence of Equilibrium in Generalized Games with Abstract Convexity Structure

The aim of this paper is to prove the existence of equilibrium for generalized games or abstract economies in contexts where the convexity conditions on strategy spaces and preference correspondences are relaxed and an arbitrary number of agents is considered. The results are based on a fixed-point theorem in which the convexity condition on sets and images of correspondences is replaced by a general notion of abstract convexity, called mc-spaces, generalizing the notions of simplicial convexity, H-spaces, and G-convex spaces.     

关于随机一致凸性

致力于随机一致凸性概念的进一步探讨．首先,通过一个特殊的层次剖分指出对任意的随机赋范模而言随机凸性模都有良好定义,从而改进了近期的文献中许多已知的结果．然后,提出并研究了一种与随机一致凸性密切相关的新性质,从一个新的角度阐述了随机一致凸性的复杂性．     

二元凸函数的判别条件

给出了二元凸函数的定义,导出了二元凸函数的判别条件,该判别条件由二元函数的二阶导数给出.用二元凸函数的判别条件和半正定的(半负定)矩阵的性质,得到了二元二次多项式凸性的简单判别形式.     

可微广义凸规划的最优充要条件

利用Bector定义的广义凸函数——univex函数,讨论可微广义凸规划和可微多目标广义凸规划的Kuhn-Tucker最优充要条件。     

$\beta$阶星象函数和凸象函数的几个充分条件的扩展

本文目的是研究了两个新算子$\mathcal{E}_{\alpha, \lambda}^{\gamma}$和$H_{m}^{l}(\alpha_1)$的星形和凸性的几个充分条件, 分别与定义在单位圆盘的广义Mittag-Leffler函数$E_{\alpha, \lambda}^{\gamma}$和广义超几何函数有关.本文得出的结果与早期的一些已知结果建立联系.     

The Forcing Convexity Number of a Graph

For two vertices u and v of a connected graph G, the set I(u,v) consists of all those vertices lying on a u-v geodesic in G. For a set S of vertices of G, the union of all sets I(u,v) for u, v S is denoted by I(S). A set S is a convex set if I(S) = S. The convexity number con(G) of G is the maximum cardinality of a proper convex set of G. A convex set S in G with |S| = con(G) is called a maximum convex set. A subset T of a maximum convex set S of a connected graph G is called a forcing subset for S if S is the unique maximum convex set containing T. The forcing convexity number f(S, con) of S is the minimum cardinality among the forcing subsets for S, and the forcing convexity number f(G, con) of G is the minimum forcing convexity number among all maximum convex sets of G. The forcing convexity numbers of several classes of graphs are presented, including complete bipartite graphs, trees, and cycles. For every graph G, f(G, con) con(G). It is shown that every pair a, b of integers with 0 a b and b is realizable as the forcing convexity number and convexity number, respectively, of some connected graph. The forcing convexity number of the Cartesian product of H × K ₂ for a nontrivial connected graph H is studied.     

Depth-Optimized Convexity Cuts

This paper presents a general, self-contained treatment of convexity or intersection cuts. It describes two equivalent ways of generating a cut—via a convex set or a concave function—and a partial-order notion of cut strength. We then characterize the structure of the sets and functions that generate cuts that are strongest with respect to the partial order. Next, we specialize this analytical framework to the case of mixed-integer linear programming (MIP). For this case, we formulate two kinds of the deepest cut generation problem, via sets or via functions, and subsequently consider some special cases which are amenable to efficient computation. We conclude with computational tests of one of these procedures on a large set of MIPLIB problems.     

Generalized Monotonicity of Subdifferentials and Generalized Convexity

Characterizations of convexity and quasiconvexity of lower semicontinuous functions on a Banach space X are presented in terms of the contingent and Fréchet subdifferentials. They rely on a general mean-value theorem for such subdifferentials, which is valid in a class of spaces which contains the class of Asplund spaces.     

Optimality Conditions and Duality in Nondifferentiable Minimax Fractional Programming with Generalized Convexity

We establish sufficient optimality conditions for a class of nondifferentiable minimax fractional programming problems involving (F, α, ρ, d)-convexity. Subsequently, we apply the optimality conditions to formulate two types of dual problems and prove appropriate duality theorems. The authors thank the referee for valuable suggestions improving the presentation of the paper.     

关于$\Gamma$函数的一个凸性结果及其应用

利用Γ函数和它的对数微商的一些性质以及Laplace变换的卷积定理,Γ函数的一个凸性结果被获得．作为应用,著名的Wallis不等式被改进．     

Convexity of Domains of Riemannian Manifolds

In this paper the problem of the geodesic connectedness and convexity ofincomplete Riemannian manifolds is analyzed. To this aim, a detailedstudy of the notion of convexity for the associated Cauchy boundary iscarried out. In particular, under widely discussed hypotheses,we prove the convexity of open domains (whose boundaries may benondifferentiable) of a complete Riemannian manifold. Variationalmethods are mainly used. Examples and applications are provided,including a result for dynamical systems on the existence oftrajectories with fixed energy.     

Convexity and marginal vectors

In this paper we construct sets of marginal vectors of a TU game with the property that if the marginal vectors from these sets are core elements, then the game is convex. This approach leads to new upperbounds on the number of marginal vectors needed to characterize convexity. Another result is that the relative number of marginals needed to characterize convexity converges to zero. Received: May 2002     

Convexity in Scheduling Problems

凸性在连续性最优化理论中起着重要的作用．它在离散性最优化中的相应概念尚待研究．本文运用差分和次梯度的概念给出排序问题中离散凸性的描述，并指出凸性在构造最优排序中的重要性．     

Hahn-Banach定理在凸性模定义中的应用

该文利用Ｈａｈｎ Ｂａｎａｃｈ定理得到了凸性模定义中若干等式的证明,并且指出对维数不小 于２的实线性赋范空间犡,有类似的等式成立。     

Convexity and Haar null sets

It is shown that for every closed, convex and nowhere dense subset of a superreflexive Banach space there exists a Radon probability measure on so that for all . In particular, closed, convex, nowhere dense sets in separable superreflexive Banach spaces are Haar null. This is unlike the situation in separable nonreflexive Banach spaces, where there always exists a closed convex nowhere dense set which is not Haar null.

     

Propagation of Convexity by Markovian and Martingalian Semigroups

We study the propagation of convexity by positive Markovian semigroups Qt on R^* ₊ which are also Martingalian (i.e. Qt Id = Id). This question is related to the management of the volatility risk in theoretical finance. We exhibit a new duality between Markovian semigroups which is an instance of T. Liggett's h-duality. In the continuous case we give a characterization theorem of the infinitesimal generators of such semigroups, and even a Lévy–Kintchine type decomposition. We give some applications to the s.d.e. dSit = ( StdBt with B standard brownian motion.